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6 results

Quantum Measurement
  • Theory and Practice
  • Andrew N. Jordan, Irfan A. Siddiqi
  • Published online:
    10 May 2024
    Print publication:
    15 February 2024
  • This book adopts a novel, physics-first approach to quantum measurement, using physical experiments as the basis to describe the underlying mathematical formalism. Topics covered include weak measurements, quantum measurement reversal, quantum trajectories and the stochastic path integral formalism. The theory of quantum measurement is also covered in detail, including discussion of how it can be tested and demonstrated in a laboratory: how to build quantum-limited amplifiers, fundamental noise limits imposed on measurement by quantum mechanics, and the design of superconducting circuits. This text is an excellent introduction for students with a basic understanding of quantum mechanics wanting to learn more about measurement theory, and the inclusion of a wide selection of end-of-chapter exercises make this book ideal for emerging courses on the topic. Key chapters introducing the foundations of quantum computing and the history of measurement theory are equally accessible to a broader, less specialised audience.

Quantum Processes and Measurement
  • Theory and Experiment
  • Claude Fabre
  • With contributions by Rodrigo G. Cortiñas
  • Published online:
    27 July 2023
    Print publication:
    10 August 2023
  • This accessible and self-contained text presents the essential theoretical techniques developed to describe quantum processes, alongside a detailed review of the devices and experimental methods required in quantum measurement. Ideal for advanced undergraduate and graduate students seeking to extend their knowledge of the physics underlying quantum technologies, the book develops a thorough understanding of quantum measurement theory, quantum processes and the evolution of quantum states. A wide range of basic quantum systems are discussed, including atoms, ions, photons, and more complex macroscopic quantum devices such as opto-mechanical systems and superconducting circuits. Quantum phenomena are also covered in detail, from entanglement and quantum jumps, to quantum fluctuations in optical systems. Numerous problems at the end of each chapter problems enable the reader to consolidate key theoretical concepts and to develop their understanding of the most widely-used experimental techniques.

  • A NATURAL DEDUCTION SYSTEM FOR ORTHOMODULAR LOGIC

  • Part of
  • ANDRE KORNELL
  • Journal:
    The Review of Symbolic Logic , First View
    Published online by Cambridge University Press:
    10 July 2023, pp. 1-40
    • Article
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  • Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with exactly one semantics for propositional formulas that use negation, conjunction, and implication. In particular, implication must be interpreted as the Sasaki arrow, which satisfies the deduction theorem in this logic. As an application, this deductive system is extended to two systems of predicate logic: the first is sound for Takeuti’s quantum set theory, and the second is sound for a variant of Weaver’s quantum logic.

  • 8 - Quantum Computing

  • Juan José García Ripoll
  • Book:
    Quantum Information and Quantum Optics with Superconducting Circuits
    Published online:
    04 August 2022
    Print publication:
    18 August 2022, pp 198-238

  • Summary

    We discuss the building blocks of a universal quantum computer within the circuit model of computation and how this is implemented using superconducting quantum circuits. In particular, we discuss, one by one, the creation of quantum registers, resetting of quantum bits, qubit measurements, single-qubit operations, and universal two-qubit gates, and how these are all implemented using the tools from earlier chapters. We discuss how to calibrate the errors in the qubits and in the operations, assigning them complete descriptions via positive maps. We explain how these errors can be corrected and how to implement a fault-tolerant quantum computer, focusing on the paradigm of stabilizer codes and the surface code in particular. We close with a discussion on the outlook for quantum computers in the near term and the NISQ paradigm of computation.

  • 3 - Interaction Effects

  • from Part II - Interacting Bose Gas
  • Hui Zhai, Tsinghua University, Beijing
  • Book:
    Ultracold Atomic Physics
    Published online:
    30 January 2021
    Print publication:
    25 February 2021, pp 73-117

  • Summary

    1. Define Bose-Einstein condensation in an interacting boson system in term of macroscopic occupation.

    2. Introduce the Gross-Pitaevskii equation and its applicable conditions.

    3. Derive the hydrodynamic equations and various physical consequences of the hydrodynamics with or without harmonic trap.

    4. Introduce sound wave and emphasize the difference between the wave behavior and the diffusive behavior.

    5. Introduce the criterion for superfluidity and determine the superfluid critical velocity.

    6. Introduce two-fluid hydrodynamics.

    7. Introduce the Bogoliubov theory.

    8. Introduce various concepts related to quasi-particle, including ground state as vacuum of quasi-particles, the zero-point energy of quasi-particle, quasi-particle lifetime and vacuum fluctuation.

    9. Introduce healing length as the characteristic length scale for low-energy physics of an interacting Bose condensate.

    10. Summarize the difference between an interacting and non-interacting Bose condensate.

    11. Introduce the Bragg spectroscopy.

    12. Show that the Bogoliubov theory fails in one-dimension due to the infrared divergence.

    13. Discuss the basic idea of the Bethe-ansatz solution and the Tonks-Girardeau limit.

    14. Introduce scale invariant quantum gases.

    15. Introduce the Josephson effect and the self-trapping as two different transport phenomena driven by phase coherence.

    16. Discuss the conjugate relation between the relative phase fluctuation and the relative particle number fluctuation, and show strong enough phase fluctuation renders the system into a Fock state.

    17. Discuss an example of quantum measurement that can project two independent condensates to a coherent superposition state.

    18. Discuss interference effects in density and density-density correlations.

    19. Discuss the relation between the instability of the Sch\"odinger Cat state and the stability of symmetry breaking.

  • 3 - Basics of Quantum Theory

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 31-49

  • Summary

    This chapter is intended to introduce some basic notions of quantum theory needed in the subsequent chapters for the reader who is not familiar with them. Quantum mechanics is a fundamental physics subject that studies the phenomena at the atomic and subatomic scales. This chapter introduces the required mathematical tools and presents the postulates mainly through their mathematical formalisms. The physics interpretation of these is only very briefly discussed.